monitoring system for the online … · en général, une pile à combustible est définie comme un...
TRANSCRIPT
UNIVERSITÉ DE MONTRÉAL
MONITORING SYSTEM FOR THE ONLINE ESTIMATION OF THE
INTERNAL PARAMETERS OF A MICROBIAL FUEL CELL OPERATED
INTERMITTENTLY
JAVIER DARIO CORONADO
DÉPARTEMENT DE GÉNIE CHIMIQUE
ÉCOLE POLYTECHNIQUE DE MONTRÉAL
MÉMOIRE PRÉSENTÉ EN VUE DE L’OBTENTION
DU DIPLÔME DE MAÎTRISE ÈS SCIENCES APPLIQUÉES
(GÉNIE CHIMIQUE)
NOVEMBRE 2013
© Javier Dario Coronado, 2013.
UNIVERSITÉ DE MONTRÉAL
ÉCOLE POLYTECHNIQUE DE MONTRÉAL
Ce mémoire intitulé :
MONITORING SYSTEM FOR THE ONLINE ESTIMATION OF THE INTERNAL
PARAMETERS OF A MICROBIAL FUEL CELL OPERATED INTERMITTENTLY
présenté par : CORONADO Javier Dario
en vue de l’obtention du diplôme de : Maîtrise ès Sciences Appliquées
a été dûment accepté par le jury d’examen constitué de :
M.SRINIVASAN Bala, Ph. D., président
M. PERRIER Michel, Ph. D., membre et directeur de recherche
M. TARTAKOVSKY Boris, Ph. D., membre et codirecteur de recherche
Mme. WOODWARD Lyne, Ph. D., membre
iii
ACKNOWLEDGEMENT
Well, when it comes down to saying thanks, I just open my heart to all those I am grateful
to. I have always thought that gratefulness only achieves its real value when it is communicated
from the heart. I will only translate my acknowledgement words for you, Michel and Boris.
Please try the Spanish version, it is much more beautiful.
Some years ago, I had the chance to read a book in Strategy consulting that finished by
giving an advice: "Wherever you go in life, always find a mentor". Recently, life gave me the
chance to add 2 very special people to a very long list of very beloved mentors: Michel, and
Boris. Michel: without realizing it, you brought fun to my life in a moment in which it was
actually difficult to find. I will always be grateful to you for having trusted me when I most
needed it. Simply, THANK YOU SO MUCH! Boris: if it was not for your advice, and respect
(patience!) for my ideas (passionate, though not always structured), besides all the trust you
always had in my work, half of the results in this document would have never been possible. I
will always be grateful for your unconditional support.
A la hora de los agradecimientos, no suelo guardarme nada. Quizás algunos lo sepan,
otros quizás no, pero soy un convencido de que la gratitud sólo alcanza su verdadera grandeza
cuando se expresa de corazón. Por ello, estas palabras son para ustedes:
Hace unos años, tuve la oportunidad de leer un libro de estrategia que en su último
capítulo aconsejaba: “a donde vayas, busca siempre un mentor”. Más tarde en la vida caí en
cuenta que siempre he gozado de excelentes mentores. Al nacer, la vida me bendijo con los que
han sido mis 2 mayores pilares: papá y mamá. A ustedes les debo todo cuanto soy. Este paso en
mi vida se los comparto, como les he compartido muchos otros. Sin duda, de no ser por todo lo
que ustedes me inculcaron, hoy por hoy yo no sería quien soy.
Más recientemente, la vida trajo a mí dos personas que desde ya hacen parte de esa lista
de espectaculares mentores: Michel y Boris. Michel: sin saberlo, trajiste diversión a mi vida en
un momento en el que me era difícil encontrarla. Siempre te estaré agradecido por haberme dado
un voto de confianza cuando más lo necesitaba. Sencillamente, ¡MUCHAS GRACIAS! Boris: de
no ser por tus consejos, tu respeto (¡y paciencia!) por mis ideas (apasionadas, más no siempre
estructuradas), además de toda la confianza que depositaste en mi trabajo, la mitad de los
iv
resultados en este documento no hubieran sido posibles. Siempre te estaré agradecido por todo tu
apoyo incondicional.
A toda la colonia colombiana en Polytechnique (¡todos!), muchas gracias por muy
agradables momentos juntos. Quebeca: si no me hubiera contigo en aquel ya lejano 2010, no
hubiese caido en cuenta de que aún tenía por descubrir una de mis grandes pasiones en la vida: la
ingenieria química. ¡Gracias!
Un párrafo aparte para quien ha sido mi compañero de batalla en todas éstas: ¡Chucho! Mi
hermano, si no hubiera chupado de su sangre todos estos años, nada de esto sería posible. Gracias
por toda su paciencia y tolerancia. Yo sé que no es fácil lidiar conmigo. Usted lo sabe… Estoy
trabajando en un milagro del que usted hace parte integrante. Si mi intuición no me engaña, la
vida nos depara aún muchas otras batallas de las cuales sé que habremos de salir vencedores.
Por último, más no por ello menos importante: ¡Tú! Sí… ¡Tú! ¡Ángela! Este triunfo es tan
tuyo como mío… Tú eres la responsable de todos y cada uno de los anteriores párrafos. Nunca
antes dediqué un documento a nadie. Bueno, ¡pues éste es para ti! No me alcanzan las palabras
para darte las gracias…
¡MUCHAS GRACIAS A TODOS!
v
RÉSUMÉ
Cette étude décrit l'opération des Piles à Combustible Microbiennes (PCMs) avec la
connexion intermittente de la résistance externe (mode R-PWM). L'étude est composée de 2
sections : la première décrit l'opération de la PCM à basses et hautes fréquences, avec différents
taux de connexion/déconnexion de la résistance externe. La deuxième partie rejoint le mode de
fonctionnement RPWM à la solution analytique d'un Modèle de Circuit Équivalent (MCE), afin
de développer une procédure de supervision en ligne. Cette stratégie rend le suivi périodique des
paramètres internes de la PCM possible.
Quant à la première partie du projet, l'analyse des profils de tension acquis démontrent la
présence de composants dynamiques lents et rapides. Ceux-ci peuvent être décrits par un modèle
de circuit équivalent simple, qui est d'ailleurs approprié pour des applications comme la
commande de procédés. Aux fréquences d'exploitation plus élevées que 100 Hz, une amélioration
considérable de la performance des PCMs est observée, avec une augmentation du 22 % au 43 %
de la puissance de sortie, en comparaison avec l'opération de la PCM avec sa résistance externe
continuellement connectée.
Basé sur les dynamique identifiées pour la PCM à basse et haute fréquence, la solution
analytique pour le modèle de circuit équivalent est ensuite utilisée comme base pour développer
une stratégie de supervision en ligne. L'algorithme permet le calcul en ligne des paramètres
internes de la PCM. Pour valider l'exactitude des valeurs estimées, les profils de tension
électrique à bas et haute fréquence sont générés et statistiquement comparés aux profils réels de
tension de la PCM. Quand les 2 profils sont comparés, des erreurs quadratiques moyenne de
5.26e-4
sont obtenues pour les profils de basse fréquence. À haute fréquence, l'erreur est 9.69e-6
.
Par ailleurs, les estimations en ligne des paramètres internes sont comparées à des paramètres
calculés hors ligne. Les évolutions observées sont en effet semblables, même si les valeurs
diffèrent.
La stratégie de supervision en ligne a été testée sous 2 conditions d'opération différentes :
d'abord, une PCM a été utilisé dans pour étudier l'évolution des paramètres en réponse aux
changements de la charge organique. De plus, une deuxième PCM a été construite pour faire le
suivi périodique de l'évolution des paramètres internes dans le temps, du démarrage de la PCM à
sa maturité.
vi
ABSTRACT
This research study describes the operation of a Microbial Fuel Cell (MFC) under pulse-
width modulated connection of the external resistor (RPWM mode). The study is composed of 2
main sections: the first one describes the MFC operation at low and high frequencies, and under
varying periods of external resistance connection/disconnection or duty cycle (D). The second
part blends the RPWM mode of operation to the analytical solution of a proposed Equivalent
Circuit Model (ECM) in order to develop an on-line monitoring procedure. This monitoring
strategy allows the periodic follow-up of the MFC internal parameters.
Regarding the first part of this project, the analysis of the output voltage profiles acquired
during R-PWM tests showed the presence of slow and fast dynamic components, which can be
described by a simple equivalent circuit model (ECM) suitable for process control applications.
At operating frequencies above 100 Hz a noticeable improvement in MFC performance was
observed with the power output increase of 22–43% as compared to MFC operation with a
constant external resistance.
Based on the identified dynamics for the MFC dynamics at low and high frequency, the
analytical solution for the equivalent circuit model is used as a basis for an on-line monitoring
strategy. This algorithm allows the online estimation of the MFC internal parameters. To validate
the accuracy of the estimations, low and high frequency voltage profiles are generated and
statistically compared to actual voltage profiles for the MFC. When actual and online estimated
profiles are compared, mean square errors of 5.26e-4 for low frequency profiles, and 9.69e-6 for
high frequency profiles were obtained. On-line estimations of the MFC internal parameters are
also compared to off-line estimated parameters, and similar evolution trends are observed.
The on-line monitoring strategy was tested under 2 different operating conditions: first,
one MFC was used in under to study parameter evolution under varying organic load. Then, a
second MFC was newly built in order to make a periodic follow-up of the internal parameters'
evolution in time, from the MFC start-up to its maturity.
vii
CONDENSÉ
Introduction et objectives
Les Piles à Combustible Microbiennes (PCMs) sont considérées une solution
technologique prometteuse dans la recherche de nouvelles sources d'énergie renouvelables,
capables de remplacer des combustibles fossiles comme source d'énergie principale des humains.
En général, une pile à combustible est définie comme un dispositif électrochimique avec la
capacité de convertir l'énergie chimique directement en électricité. Quoique des réactions
chimiques ayant lieu dans des piles à combustible soient semblables à ceux ayant lieu dans des
batteries conventionnelles, la différence principale entre ces deux vient du fait que les piles à
combustible sont des systèmes ouverts où les réactifs coulent continuellement dans la pile.
Même si les PCMs ne pourront pas remplacer le pétrole dans un futur proche, leur
capacité à produire de l'énergie électrique les rend un sujet de recherche intéressant. Étant un
système bio-électrochimique, les PCMs ont déjà prouvé leur capacité à produire de l'électricité,
ainsi qu'à traiter des eaux usées (Oh, et d'autres., 2010). C'est pourquoi, des sciences multiples se
mêlent présentement dans leur étude : la microbiologie, la chimie, le génie chimique, le génie
électrique, le génie civil, ainsi que les sciences des matériaux sont en fait le cas. Néanmoins, un
des plus grands défis scientifiques est toujours lié à la modélisation et au contrôle, étant donné la
nature toujours changeante des systèmes vivants.
Ce document présente alors les résultats obtenus du projet de recherche visant à
développer un outil de supervision en temps réel pour l'analyse en ligne de la performance
électrique d'une Pile à Combustible Microbienne opérée de façon intermittente. Afin d'atteindre
cet objectif, deux tâches principales sont exécutées:
1. la caractérisation de la performance électrique de PCMs opérées de façon
intermittente en fonction de la fréquence d'opération et du ratio de
connexion/déconnexion de la résistance externe, et
2. le développement d'un outil de supervision en ligne pour évaluer les paramètres
internes électriques d'une PCM modélisée à partir d'un modèle de circuit équivalent
(MCE) simplifié.
viii
Mode R-PWM et caractérisation en fréquence
Afin d'évaluer l'effet de la connexion intermittente de la résistance externe (mode
d'opération R-PWM), deux (2) PCMs ont été opérées à plusieurs fréquences dans une plage entre
0.1 Hz et 1000 Hz. À chaque fréquence testée, Rext est connectée à la PCM pendant la première
moitié du cycle et débranché pour le reste du cycle. Ces tests ont été effectués pour des valeurs de
Rext entre 8 et 47 ohms. La tension moyenne a augmenté avec l'augmentation de fréquence,
ensuite un plateau est atteint à peu près entre 100 et 500 Hz.
Aux fréquences d'exploitation plus élevées que 100 Hz, une amélioration considérable de
la performance des PCMs est observée, avec une augmentation du 22 % au 43 % de la puissance
de sortie, en comparaison avec l'opération de la PCM avec sa résistance externe continuellement
connectée.
MCE et les dynamiques à basse et haute fréquence
À basse fréquence (~0.05 Hz) deux composants dynamiques différents sont remarqués
lors de la connexion intermittente de la résistance externe. D'abord, il y a un changement soudain
de la tension de sortie de la PCM, jusqu'à atteindre d'une certaine valeur intermédiaire. Cette
transition rapide est suivie par une courbe exponentielle, qui s'approche de la valeur stationnaire à
un taux beaucoup plus lent.
Par contre à haute fréquence (~100 Hz), seulement la dynamique rapide apparaît dans le
profil de tension de la PCM, alors que la dynamique lente disparaît et le voltage semble
essentiellement commuter entre deux niveaux. La tension la plus haute correspond à l'état de
circuit ouvert (résistance externe déconnectée). D'autre côté, la tension la plus basse correspond à
l'état de circuit fermé (résistance externe connectée). Ces deux (2) dynamiques peuvent être
décrites par un modèle de circuit équivalent (Randles le modèle, (Randles, 1947)). Ce modèle
consiste de deux résistances et une capacitance, qui permet la description des réponses de tension
de sortie lentes et rapides observées pendant les tests. Pour le modèle montré dans la ¡Error! No
se encuentra el origen de la referencia. de ce document, correspond à la tension de circuit
ouverte de la PCM (tension idéale), C représente la capacitance réelle de la MFC, R1 représente
les pertes ohmiques, alors que R2 représente les pertes par activation et par concentration de la
PCM (Yang, Zhang, Shimotori, Wang et Huang, 2012).
ix
Le MCE et la stratégie de supervision en ligne
Généralement, les propriétés électriques de systèmes bio-électrochimiques sont mesurées
au moyen des méthodes électrochimiques hors connexion comme des courbes de polarisation ou
avec des voltamètres cycliques. Bien que ces méthodes fournissent des mesures précises pour des
paramètres électriques comme la résistance interne et la capacitance, ils exigent que le système
soit pris hors ligne pour la mesure pour être précis.
Dans le but de pouvoir appliquer les principes de commande de procédé à l'amélioration
de la performance des PCMs, il est nécessaire d'avoir des outils permettant le suivi en ligne des
paramètres internes des PCMs. La stratégie de supervision proposée dans ce projet de recherche
est basée tant sur la solution analytique du modèle de circuit équivalent étudié (MCE), que sur les
profils à bas et haute fréquence retrouvés lors de l'opération intermittente de la PCM.
La stratégie de supervision en ligne a été testée pour deux (2) conditions d'opération
différentes : d'abord, l'évolution des paramètres en réponse aux changements de la charge
organique a été étudié. Ensuite, l'évolution des paramètres internes dans le temps est étudiée, en
suivant le comportement dynamique d'une PCM du démarrage à sa maturité.
L'algorithme permet en effet le calcul en ligne des paramètres internes de la PCM. Pour
valider l'exactitude des valeurs estimées, les profils de tension électrique à bas et haute fréquence
sont générés et statistiquement comparés aux profils réels de tension de la PCM. Quand les 2
profils sont comparés, des erreurs quadratiques moyenne de 5.26e-4 sont obtenues pour les
profils de basse fréquence. À haute fréquence, l'erreur est 9.69e-6. Par ailleurs, les estimations en
ligne des paramètres internes sont comparées à des paramètres calculés hors ligne.
x
TABLE OF CONTENTS
ACKNOWLEDGEMENT ............................................................................................................ III
RÉSUMÉ ........................................................................................................................................ V
ABSTRACT .................................................................................................................................. VI
CONDENSÉ .................................................................................................................................VII
TABLE OF CONTENTS ............................................................................................................... X
LIST OF TABLES ..................................................................................................................... XIII
LIST OF FIGURES .................................................................................................................... XIV
LIST OF ABBREVIATIONS .................................................................................................... XVI
CHAPTER 1 INTRODUCTION ............................................................................................... 1
1.1 Problem Definition ........................................................................................................... 2
1.1.1 Microbial Fuel Cells ..................................................................................................... 2
1.1.2 Microbial Fuel Cells and Water Treatment .................................................................. 3
1.1.3 Dynamic Systems, Process Control and Frequency Analysis ...................................... 3
1.1.4 Pulse Width Modulation (PWM) and Power Control .................................................. 4
1.2 Project Objectives ............................................................................................................ 4
1.3 Document Structure .......................................................................................................... 5
CHAPTER 2 LITERATURE REVIEW .................................................................................... 6
2.1 Biochemical Processes: an overview ............................................................................... 6
2.2 Microbial Fuel Cells Modeling: from Microbiology to Process Dynamics ..................... 7
2.3 Microbial Fuel Cells: Performance Optimization, Energy Storage, and Control ............ 7
2.3.1 Performance optimization ............................................................................................ 8
2.3.2 Energy Harvesting and Storage .................................................................................... 8
2.3.3 Control and Optimization ............................................................................................. 9
xi
CHAPTER 3 MATERIALS AND METHODS ...................................................................... 12
3.1 MFC design, inoculation, and operation ........................................................................ 12
3.2 External resistance connection (R-PWM Mode of Operation) ...................................... 13
3.3 Frequency and Duty Cycle Tests ................................................................................... 14
3.4 Perturbation/Observation algorithm ............................................................................... 15
3.5 Numerical methods ........................................................................................................ 15
CHAPTER 4 MFC OPERATION WITH PULSE-WIDTH MODULATED CONNECTION
OF REXT 16
4.1 Frequency Characterisation of MFCs ............................................................................ 16
4.2 Dynamic Response of MFCs at Low and High Frequency ............................................ 17
4.3 The Equivalent Circuit Model Explained ....................................................................... 19
4.3.1 The High Frequency Profile ....................................................................................... 20
4.3.2 Power Analysis for High Frequency Operation ......................................................... 21
4.3.3 The Low Frequency Profile ........................................................................................ 22
4.4 The Proposed Equivalent Circuit as a Modeling Tool for MFCs .................................. 22
4.5 Duty Cycle (D) Characterisation of the MFCs ............................................................... 23
CHAPTER 5 ECM APPLICATION FOR ONLINE MONITORING AND PARAMETER
ESTIMATION OF A MFC ........................................................................................................... 28
5.1 Monitoring Procedure: from Electrical Modeling to Online Monitoring Tool .............. 28
5.2 Parameter Estimation and Online Monitoring Tests ...................................................... 30
5.2.1 MFC Internal Parameters Variation as a Function of Organic Load ......................... 30
5.2.2 MFC Internal Parameters Variation as a Function of Time ....................................... 37
CHAPTER 6 CONCLUSION AND RECOMMENDATIONS .............................................. 43
6.1 Conclusions .................................................................................................................... 43
6.2 Recommendations .......................................................................................................... 44
xii
6.2.1 Characterisation of MFC performance under a wider range of frequencies .............. 44
6.2.2 The online monitoring strategy as a sensor for process control ................................. 44
A personal quote ......................................................................................................................... 45
BIBLIOGRAPHY ......................................................................................................................... 46
xiii
LIST OF TABLES
Table 1 A comparison of average currents, power outputs and Coulombic Efficiencies (CE)
obtained during - PWM and Perturbation/Observation tests carried out at two influent
acetate concentrations. ........................................................................................................... 25
Table 2 Mean Square Errors for UMFC estimated profiles at different organic loads .................. 32
Table 3 Summary of Standard Deviations for Online and Offline Estimations............................. 37
Table 4 Mean Square Errors for UMFC estimated profiles during organic maturation of MFC ..... 39
xiv
LIST OF FIGURES
Figure 1. Schematic diagrams: (A) experimental setup, and (B) electrical circuit used in all tests.
................................................................................................................................................ 13
Figure 2. Average external voltage ( ) as a function of Rext connection / disconnection
frequency. A – MFC-1 tests with 15 min and 1 h intervals between frequency changes; B –
MFC-2 tests performed with frequency changes at 1 h intervals. .......................................... 16
Figure 3. Profiles of MFC voltage ( ) measured at connection / disconnection
frequencies of (A) 0.05 Hz (D=75%) and (B) 100 Hz (D=90%). .......................................... 17
Figure 4. MFC Equivalent Circuit Model (ECM) .......................................................................... 19
Figure 5. High frequency profile of a MFC operated under R-PWM mode ................................... 21
Figure 6. Voltage profile for a MFC operated at low frequency .................................................... 22
Figure 7. MFC Power outputs of MFC-1 (A) and MFC-2 (B) as a function of their duty cycles.
Power output at D=100% corresponds to MFC operation with fixed external resistance. All
D-tests were carried out at a frequency of 500 Hz. ................................................................ 24
Figure 8. UMFC profile at low frequency operation ........................................................................ 29
Figure 9 Flow rates of acetate stock solution ................................................................................. 31
Figure 10 UMFC voltage profiles at nominal or higher influent concentration (≥ 900 mg L-1
)....... 32
Figure 11 UMFC voltage profiles at low influent concentration (450 mg L-1
) ................................ 33
Figure 12 Results for on-line and off-line estimation of R1 ........................................................... 34
Figure 13 Results for on-line and off-line estimation of R2 ........................................................... 34
Figure 14 Comparison of Rint estimations (on-line and off-line) with experimentally measured
values based on polarization tests. ......................................................................................... 35
Figure 15 Results of on-line and off-line estimation of Uoc. .......................................................... 36
Figure 16 Results of online and offline estimation of C. ............................................................... 37
Figure 17 UMFC voltage profiles 18 hours after the MFC start-up. ................................................ 38
xv
Figure 18 UMFC voltage profiles 1 week after the MFC start-up. ................................................... 38
Figure 19 UMFC voltage profiles 20 days after the MFC start-up. .................................................. 39
Figure 20 R1 and R2 evolution in time. ........................................................................................... 40
Figure 21 Rint evolution in time. ..................................................................................................... 41
Figure 22 UOC evolution in time. ................................................................................................... 41
Figure 23 Capacitance C evolution in time. ................................................................................... 42
xvi
LIST OF ABBREVIATIONS
D Duty Cycle
DC Direct Current
ECM Equivalent Circuit Model
MCE Model de Circuit Équivalent
MSE Mean Square Error
MFC Microbial Fuel Cell
MPPT Multi-unit Maximum Power Point Tracking
PCM Pile à Combustible Microbienne
P/O Perturbation / Observation Algorithm
PWM Pulse Width Modulation
R-PWM Resistance-Pulse Width Modulation mode
1
CHAPTER 1 INTRODUCTION
Just like every living form on Earth, human beings are constantly changing. That is why,
evolving has always been deep in our nature. Nevertheless, growth transitions, like adolescence,
often cause problems to humans. Adaptive behavior is needed in order to catch up with new
circumstances. Moments of transition always represent great challenges for human's creativity
and adaptability. Nowadays, humanity is hugely concerned by a great moment of transition that
challenges our scientific and technological knowledge. Maybe for the very first time in our young
history, the challenge embraces human's capacity to sustainably live in a society.
Human's need for sustainable development imperatively demands: 1) the change of our
highly non-renewable and contaminating energy sources by renewable ones; 2) the optimization
of wastewater treatment procedures, as well as 3) the efficiency improvement of the energy
recovery techniques currently in use in industry. Beautifully, the challenge has not only attracted
the attention of scientists around the world, but it has been the main reason for multiple television
series and science fiction films for the last two decades. AVATAR, IRON MAN, BATMAN or
PRISON BREAK are just a small proof of it.
Microbial Fuel Cells (MFCs) are considered a promising technological solution that could
help tackling the challenges previously mentioned. Even though MFCs are not yet considered an
energy source capable of replacing petroleum based fuels in a foreseeable future, their capacity
for electrical energy recovery make them an interesting subject for research. As a bio-
electrochemical system, MFCs have already proven their capacity to generate electricity while
biochemically treating wastewater (Oh, et al., 2010). Hence, multiple sciences have merged in
their study: microbiology, chemistry, chemical, civil, and electrical engineering, as well as
material science. Nonetheless, one of the biggest scientific challenges is always tied to the
modeling and control of the continually changing nature of the oxidation-reduction reactions
taking place in the bioreactors.
For the case of study described in this document, chemical and electrical engineering
gather together once again in the quest for a beautiful goal: modeling, optimizing and controlling
MFCs. This fusion have proven extraordinary results for science in the past, giving even birth to
heat transfer modeling by means of basic first order electrical circuits (Bergman, Lavine,
Incropera, & Dewitt, 2012). So, just as heat exchangers were initially studied using electrical
2
models to later become a major energy recovery tool in industrial process plants, electrical
circuits are currently used as a modeling tool in the research to attain a major understanding of
inherently living systems such as the MFCs.
Therefore, the research presented in this document looks forward to improving human's
understanding of MFCs by using some engineering tools to study them, while improving their
performance. For sure, MFCs are foreseen as a feasible technology for electrical energy recovery
in the search for reducing electrical energy consumption in wastewater treatment plants. Power
efficiency improvement has become a common issue in current research studies.
Hereafter, some major concepts are presented. These represent the major scientific
framework inside which this research has been developed. Besides, they create a technical
framework prior to introducing the main objectives of this research project.
1.1 Problem Definition
1.1.1 Microbial Fuel Cells
In general, a fuel cell is defined as an electrochemical device with the capacity to directly
convert chemical energy into electricity. Though chemical reactions taking place in fuel cells are
similar to those occurring in conventional batteries, the main difference between these two arises
from the fact that fuel cells are open systems where reactants are continually flowing into the cell.
Oxidation-Reduction reactions take place in fuel cells. Oxidation takes place at the anode,
known by convention as the negative electrode, while reduction takes place at the cathode, the
positive electrode. When reaction takes place, electrons are liberated, allowing current to flow
between both electrodes. To foster ion exchange, the electrodes are commonly placed in an
electrolyte solution.
In the particular case of MFCs, electricigenic microorganisms work as the catalysers of
the bio-electrochemical reaction. Wastewater containing dissolved organic matter may be used as
fuel for the cell. The organic matter is degraded by these microorganisms, which need this
material for their biological cycle that comprises their metabolism, growth and reproduction.
3
1.1.2 Microbial Fuel Cells and Water Treatment
MFCs are a new type of bioreactors with a proven capacity for treating a large variety of
highly diluted organic matter while producing electricity (Logan & Regan, 2006); (Debabov,
2008).
In general, MFCs are composed of two chambers: the anaerobic anode, and the aerobic
cathode. These two are separated by an ion conducting membrane. Anaerobic respiring bacteria
attached to the anode work as catalysers, while oxidizing organic matter and producing both
protons and electrons. The electrons are transferred to the anode, where they subsequently pass
through an external electrical circuit to produce current. Protons migrate through the membrane
to the cathode, where they react with oxygen to produce water.
Research on MFCs may be divided into three main areas (Oh, et al., 2010):
1) the reactor design in order to reduce unwanted biomass production in wastewater
treatment,
2) the study of the microbial communities participating in the bio-electrochemical
process, and
3) modeling, control and optimization of operating conditions.
One of the main goals of applying control and optimization techniques is the
enhancement of MFCs low power density (Logan, et al., 2006).
1.1.3 Dynamic Systems, Process Control and Frequency Analysis
Systems in engineering are studied in two different ways: dynamically and statically.
Dynamic models comprise both transient and steady state responses, while static systems are
commonly studied in order to identify the steady state response of a given system. Dynamic
models are commonly represented by differential equations in a time based space, while different
frequency space transformations (Fourier, Laplace, etc.) are highly used in order to make stability
analysis in a frequency based space.
Commonly, when a dynamic model is achievable, control laws are established in order to
improve the performance of the system. In the case of biochemical systems, as it is the case for
MFCs, models are difficult to develop due to their highly non-linear time variant inherent
characteristic.
4
In the case of MFCs, electrical studies have been carried out neglecting fast dynamics
related to electrical properties of the MFCs (Aelterman, Versichele, Marzorati, Boon, & &
Verstraete, 2008); (Woodward, Perrier, Srinivasan, & Tartakovsky, 2009)). These research
studies model MFCs as electrical systems by means of exclusively resistive circuits. More
recently, MFCs electrical dynamics has been paired to first order circuits (Yang, Zhang,
Shimotori, Wang, & Huang, 2012). Furthermore, periodic operation of MFCs is currently being
studied in order to improve MFCs power generation capacity, as well as for modelling their
transient response (Grondin, Perrier, & Tartakovsky, 2012); (Coronado, Perrier, & Tartakovsky,
2013).
When dynamic systems are modeled, low and high frequency analysis become very useful
as a stability analysis and modeling tool. Besides, frequency based methods make it possible to
accurately establish the frequency response of electrically modeled systems. Different frequency-
based methods used in process control comprise: bode diagrams, root-locus representation, and
Nyquist stability analysis, among others.
1.1.4 Pulse Width Modulation (PWM) and Power Control
Pulse Width Modulation (PWM) is a control technique commonly used for power control
in power electronic applications. In these applications, the average power to a load is controlled
by commuting on and off an electronic power switching device. As voltage (and current) coming
out of the power source are modulated (switched 'on' and 'off'), power is controlled so maximum
power feed may be achieved, subsequently optimizing the energy furnished to the attached load.
Duty cycle (D) corresponds to the portion of 'on' time to the period of time. It is
commonly expressed in percent. Generally, low power corresponds to a low duty cycle, while
100% means that the circuit is always 'on'. PWM is a well-known electrical control technique
already under study on MFCs, mainly looking forward to enhancing the system's energy storage
capacity (Wu, Biffinger, Fitzgerald, & Ringeisen, 2011).
1.2 Project Objectives
General Objective: To develop a real-time process monitoring tool for the on-line analysis
of the electrical power performance of a Microbial Fuel Cell operated intermittently.
5
Specific Objectives:
1) Characterize the performance of a MFC operated intermittently as a function of the
external resistance connection/disconnection rate (variable frequency and duty cycle).
2) Develop an on-line monitoring tool for estimating electrical internal parameters of a MFC
modeled using a simplified equivalent circuit model (ECM).
1.3 Document Structure
After presentation the literature review and the material and methods that give a frame to
this project, the main research results are presented in chapters 4 and 5.
Chapter 4 mainly explains the proposed method of operation for the MFC (R-PWM). Two
main studies are presented: the characterisation of MFC power performance to an intermittent
operation at low and high frequencies, as well as the MFC power performance in response to
varying period of connection or duty cycle (D). Besides, the Equivalent Circuit Model (ECM) is
first explained, creating the links between this model and the MFC operation at low and high
frequencies.
Chapter 5 describes the way in which the analytical solution of the ECM is used in order
to achieve an on-line monitoring and parameter estimation algorithm. The results for 2 different
experiences are presented. First, the on-line monitoring strategy is used to make the follow-up of
MFC internal parameters while organic load is periodically varied. Second, a MFC was newly
built and followed-up by means of the propose on-line parameter estimation procedure. The
evolution of parameters in time is then evaluated.
Finally, the conclusions to the study presented in this document are mainly focused on the
results presented in Chapters 4, and 5.
6
CHAPTER 2 LITERATURE REVIEW
This literature review is composed of three main sections. The first one makes a brief
overview of the principles of biochemical processes. Then, the second section describes how
modeling of MFCs has evolved in time, while the last section summarizes some state-of-the-art
studies on MFCs optimization and control.
1.4 Biochemical Processes: an overview
Basically, a biochemical process is focused on the growth of certain type of
microorganism. In order for a microorganism to grow, nutrients must be fed at favourable
environmental conditions (temperature, pH, etc.). Hence, while the biochemical process takes
place, a carbon source (substrate) is consumed in order to produce such products as oils, cheeses,
enzymes, amino acids, ethanol or biogas, among others, depending on the main interest of the
corresponding industry.
Modeling a biochemical system is a critical stage prior to its optimization and control. A
biochemical reaction scheme is initially established in order to describe the biological and
chemical reactions that take place in the bioreactor. Reactions belonging to the reaction scheme
may include: microorganisms' growth, product generation, and microorganisms' mortality.
Schemes are normally completed (Bastin, et al., 2001) by including the reactions' rates and the
consumption yields. Reaction kinetics are often modelled by means of a Monod model, which is
based on the Michaelis-Menten reaction kinetics (Eddy, 2003).
Reaction's schemes are completed with mass and energy balances. In fact, these schemes
make it possible to establish dynamical models for the biochemical system. Mass balances are
highly dependent on the type of reactor used (batch, fed batch or continuous stirring tank reactor
(CSTR)). Balances are normally expressed as a function of different variables (substrates,
products or biomasses) that describe the dynamics of the system. Finally, reaction rates are
expressed as a function of the chosen variables for simulation, control or optimization purposes.
7
1.5 Microbial Fuel Cells Modeling: from Microbiology to Process Dynamics
Microbial fuel cells (MFCs) are based on biochemical processes in which electricity is a
final product for the reacting system (scheme). The main challenge arising while modeling MFCs
is the adequate interpretation of the narrow relationship between microbial growth and
metabolism, and electricity generation and performance.
Although MFCs were initially modeled as one-population microbial systems, (Zhang &
Halme, 1995); (Marcus, Torres, & Rittmann, 2007)), more recent studies (Picioreanu, Katuri,
Head, Van Loosdrecht, & Scott, 2008) proved the need for multi-population biological models in
order to accurately understand the biological behaviour inside the bioreactors used for MFCs'
applications. Nonetheless, the complexity associated with multi-population models makes
necessary to design simplified models for control and optimization purposes.
A simplified two-population bio-electrochemical model was proposed by Pinto et al.,
(Pinto R. P., Srinivasan, Manuel,, & Tartakovsky, 2010.) for off-line process optimization. The
proposed model describes the competition of two types of microbial populations for a common
substrate in a MFC: anodophilic and methanogenic bacteria. By means of multiplicative (double-
Monod) models (Bae & Rittmann, 1996a), and Nernst based equations ("Fuel Cell Handbook,"
2005), the model proposes a dependence of electrical parameters on anodophilic biomass density,
besides proving the influence of organic load and external resistance on power output and long-
term performance.
1.6 Microbial Fuel Cells: Performance Optimization, Energy Storage, and
Control
Given their low power density (Logan, et al., 2006), researchers currently dedicate their
research work to the development of optimization strategies allowing to increase their capacity
for electrical energy production
.
8
1.6.1 Performance optimization
Different approaches are used in order to improve MFCs' performance. Some of them are
related to Material Science and focus on improving bioreactor's performance. Some others seek a
deeper understanding of the bio-electrochemical behaviour of the dynamic system.
A recent study aimed at improving bioreactor's performance demonstrates that using
extended longitudinal tubular MFCs reactors may increase power recovery and organic removal
efficiency (Kim, et al., 2011). Moreover, in (Saito, et al., 2011), the effect of carbon clothes
anodes modified with 4(N,N-dimethylamino)benzene diazonium tetrafluoroborate over MFCs'
performance is proved by demonstrating that the lowest the amount of nitrogen source in the
anode, the highest maximum power density may then be achieved.
Aelterman et al., (Aelterman, Rabaey, Pham, Boon, & Verstraete, 2006) developed some
tests with stacked microbial fuel cells in order to improve continuous electricity generation at
high voltages and currents. The study proves the capacity of their approach to increase the values
of both voltage and current, noting that microbial communities concentration are affected by the
biological and electrochemical interactions between MFCs.
Moreover, substrate consumption has been optimized by means of staging strategies. A
reactors-in-series approach (staging) (Pinto, Tartakovsky, Perrier, & Srinivasan, 2010) has
already been proven to optimize substrate consumption in a MFC. The staging strategy was used
to resemble CSTRs in series to Plug Flow Reactors (PFRs) dynamics. From the point of view of
influent treatment performance, connection in series proved to have better treatment capacities
than the connection in parallel.
1.6.2 Energy Harvesting and Storage
Electrical energy storage is also of great interest for researchers. In order for MFCs to be
able to feed electrical energy to actual electrical loads, it is necessary to increase their capacity
for electricity generation. To do so, (Dewan, Donovan, Heo, & Beyenal, 2010) have already
developed a Microbial Fuel Cell tester with the capacity to calculate the power of the MFC as a
function of the time needed to charge an external capacitance that harvests the power supplied by
9
the MFC. Power is optimized by varying the capacitor value and the charging and discharging
potentials.
The principles of electrical power switching supplies are also currently under study
looking forward to improving the energy storage capacity of stacked MFCs. Wu et al,. (Wu,
Biffinger, Fitzgerald, & Ringeisen, 2011) designed a DC/DC booster circuit in order to increase a
typical operational voltage to produce a maximum output power. Values for the DC/DC circuit
are optimized using a proposed procedure while power consumed by the circuit was reduced to a
minimum.
Similarly, Yang et al. (Yang, Zhang, Shimotori, Wang, & Huang, 2012) used a Power
Management System (PMS) in order to improve a MFC's energy harvesting capacity. Super
capacitors' impedance were optimized for maximum average harvested power, while a circuit
composed of a transformer and a DC/DC boost converter is designed to increase both voltage and
current supplied to an electrical non-resistive load. The transformer-based PMS network designed
by Yang et al. works at a lower voltage that other MFC PMS designs.
The internal equivalent circuit model used by Yang et al. (Yang, Zhang, Shimotori,
Wang, & Huang, 2012) is identical to that used by Grondin et al. (Grondin, Perrier, &
Tartakovsky, 2012), though for different research purposes, following different approaches for
the calculation of the MFC internal current.
1.6.3 Control and Optimization
Control theory is originally based on human's will to control and regulate systems just as
the human body biologically regulates itself. However, two major restrictions arise on
bioprocesses control and optimization (Bastin, et al., 2001):
1) the living nature of bioprocesses makes them difficult to model by means of already
highly developed scientific methods, and
2) the unavailability of sensors for the continuous measurement of variables such as
biomass, substrate, or product concentration.
10
Despite this, control and optimization techniques are broadly considered in the research
for strategies that give scientists a further understanding of MFCs as a bio-electrochemical
system. Both of them combined have extensively proven their capacity to identify system's
parameters by using advanced well-known mathematical methods, what makes them highly
attractive for the characterization and optimization of MFCs. Some state-of-the art studies are
presented hereafter.
While varying electrical load (impedance) attached to an MFC, Premier et al., (Premier,
Rae Kim, Michie, Dinsdale, & Guwy, 2011) proved that the automatic control of the load helps
increasing both the MFCs' power and efficiency. When comparing the results of automatically
changing the load to those obtained while letting the load fixed, an improvement of 19.73% in the
MFC's electrical power performance is obtained. Both experiences were executed for MFCs
operating at the same organic load.
Woodward et al., (Woodward, Perrier, Srinivasan, & Tartakovsky, Maximizing Power
Production in a Stack of Microbial Fuel Cells Using Multiunit Optimization Method, 2009)
developed a Multi-unit Maximum Power Point Tracking (MPPT) algorithm that calculates the
gradient using outputs of two identical MFCs. The MFCs are operated at different resistive loads
and the power difference between them indicates the direction the gradient should follow.
Although the Achilles' heel of the proposed method arises at stating that both MFCs as identical,
Woodward et al., (Woodward, Perrier, & Srinivasan, Comparison of Real-Time Methods for
Maximizing Power Output in Microbial Fuel Cells, 2010) proved that this method converges
faster than a perturbation-observation (P/O) algorithm, which varies the value of the controlled
variable in order to establish the optimal operating point.
Furthermore, Degrenne et al., (Degrenne, Buret, Allard, Bevilacqua, & P., 2012) operated
ten identical single-chamber 1.3L MFCs following a MPPT algorithm to control an electrical
converter in order to improving global MFC performance. Their MPPT algorithm mainly
consisted of the regulation of the MFC voltage to one-third of the open circuit value. The results
obtained for power output following the proposed method were quite similar to those obtained
when using a (P/O) algorithm.
Recently, external electrical circuits optimization is increasingly being used for MFC's
research. Park et al. (Park & Ren, Hysteresis controller based maximum power point tracking
11
energy harvesting system for microbial fuel cells, 2012) developed a hysteresis controller based
MFC energy harvesting system. For this case study, both an energy harvesting network and a
voltage boost converter were conceived. The proposed MPPT algorithm uses potentiometers for
the hysteresis controller. Their strategy eliminates the need for external resistances and enables
simultaneous maximum power point tracking and maximum MFC energy harvest in real-time.
Electrical circuit modeling is another strategy increasingly being studied in order to
complete the highly complex multi-population models of the MFCs. Besides estimating internal
parameters of an internal equivalent circuit model proposed, Grondin et al. (Grondin, Perrier, &
Tartakovsky, 2012) use the duty cycle principle in order to optimize power output to a fixed
resistive load.
The proposed method makes a duty cycle control based on voltage measurements for
minimum and maximum output voltages. It was proven that power output may be maximized
both under limiting or non-limiting organic load conditions, without changing the value of the
external resistance, just by intermittently connecting the electrical load based on established
voltage thresholds. This system achieved maximum power output at different duty cycle values,
while the value of the external resistive load was changed.
Another duty cycle analysis over a MFC was made by Wu et al. (Wu, Biffinger,
Fitzgerald, & Ringeisen, 2011). In this case, a duty cycle and a frequency analysis were made
over a DC/DC booster circuit connected to the studied MFC. The frequency analysis was made
from 10 to 50 kHz in order to establish the frequency at which maximum output power is
achieved from 3 stacked mini-MFCs connected in parallel. In the case of study of Grondin et al.
(Grondin, Perrier, & Tartakovsky, 2012), no frequency analysis is described, though frequencies
used are .
12
CHAPTER 3 MATERIALS AND METHODS
1.7 MFC design, inoculation, and operation
Two membrane-less air-cathode MFCs were constructed using nylon plates as described
elsewhere (Grondin et al. 2012). The anodes were 5 mm thick carbon felts measuring 10 cm × 5
cm (SGL Canada, Kitchener, ON, Canada) and the cathodes were 10 cm x 5 cm manganese -
based catalyzed carbon E4 air cathodes (Electric Fuel Ltd, Bet Shemesh, Israel). The electrodes
were separated by a nylon cloth. Two MFCs, MFC-1 and MFC-2, were built. Both MFCs had an
anodic compartment volume of 50 mL. MFC-1 contained two 10 cm x 5 cm carbon felt anodes
with a total thickness of 10 mm and two cathodes (one on each side connected by a wire) with a
total surface area of 100 cm2. MFC-2 had one 10 cm x 5 cm carbon felt anode with a thickness of
5 mm and one 50 cm2 cathode.
Each MFC was inoculated with 5 mL of anaerobic sludge with volatile suspended solids
(VSS) content of approximately 40-50 g L-1
(Lassonde Inc, Rougemont, QC, Canada) and 20 mL
of effluent from (Pinto R. , Srinivasan, Guiot, & Tartakovsky, 2011a)an operating MFC. The
MFCs were maintained at 25ºC and were continuously fed with sodium acetate and trace metal
solutions using a syringe pump and a peristaltic pump, respectively. The acetate stock solution
was composed of (in g L-1
): sodium acetate (37.0), yeast extract (0.8), NH4Cl (18.7), KCl (148.1),
K2HPO4 (64.0), and KH2PO4 (40.7). The infusion rate of the acetate stock solution was varied in
order to obtain the desired influent concentration. The trace metal solution was prepared by
adding one mL of the trace elements stock solution to 1 L of deionised water. A detailed
composition of the stock solution of the trace elements is given elsewhere (Pinto R. , Srinivasan,
Guiot, & Tartakovsky, 2011a).
13
Figure 1. Schematic diagrams: (A) experimental setup, and (B) electrical circuit used in all tests.
An influent acetate concentration of 900 mg L-1
and a hydraulic retention time of 6-7 h
were typically maintained, with an exception of the high and low-load tests, where the influent
acetate concentration was varied. For organic load characterisation purposes, 4 different organic
loads were used : 450 mg L-1
, 900 mg L-1
, 1350 mg L-1
, and 1800 mg L-1
. The mathematical
calculation of acetate flow rates from these organic loads is later explained in this document.
Figure 1A shows the schematic diagram of the experimental setup, while a detailed description
of MFC design, stock solution composition, and operating conditions can be found elsewhere
(Grondin, Perrier, & Tartakovsky, 2012).
1.8 External resistance connection (R-PWM Mode of Operation)
Pulse-width modulated connection of the external resistor (Rext) to MFC terminals was
achieved by adding an electronic switch (IRF540, International Rectifier, El Sequndo, CA, USA)
to the external electrical circuit (denoted as SW in Figure 1B, the corresponding resistance is
shown as RSW). The switch was computer-controlled using a Labjack U3-LV data acquisition
board (LabJack Corp., Lakewood, CO, USA). The data acquisition board was also used to record
MFC voltage at a maximum rate of 22,500 scans/s.
Pump 1
Pump 2
Heater
Off-gas
Pump 3
MFC
EffluentR
ecir
cula
tio
n
H2
O +
Tr
ace
Met
als
Ace
tate
RLoad
Cathode
Anode
SW-
+
UMFC
-
+
UextVMFC
Vsw
MFC
RSW
14
As shown in Figure 1B, the data acquisition board measured MFC output voltage (UMFC)
and voltage after the switch (Usw). Electrical connections corresponding to these measurements
are shown in Figure 1B as VMFC and VSW, respectively. Voltage over the resistive load (ULoad)
was calculated as the difference between UMFC and Usw (ULoad = UMFC – Usw). Electric current
was calculated as I = ULoad / RLoad by applying Ohm's law over the external load resistance
(RLoad).
For calculation purposes, the switching device was considered as an ideal switch in series
with a resistance Rsw to represent power losses in the switch. Rsw value was estimated by dividing
the voltage over the switch by the current. In the following discussion, Rext denotes the sum of the
external load connected to the circuit and the switch resistance (Rext = RLoad + Rsw) with a
corresponding external voltage Uext, as follows from the diagram shown in Figure 1B. The
voltage measurements described above and the calculation method accounted for power losses
due to the fast switching.
1.9 Frequency and Duty Cycle Tests
Frequency and duty cycle tests were carried out with either 15 min or 1 h intervals
between parameter changes. The tests were performed in a broad range of frequencies from 0.1
Hz to 1000 Hz. Duty cycle was set to 50% when frequency tests were carried out. For the duty
cycle analysis, duty cycles were varied between 5% and 100% at a constant frequency of 500 Hz.
Between the R-PWM tests, the MFCs were operated using the Perturbation/Observation
algorithm described below.
MFC performance was expressed in terms of average (per cycle) output voltage, current,
and power output. Average values per cycle were obtained as follows:
(1)
Where m(t) is either the voltage, current, or power measurements at each moment of time
t, T is the cycle duration, and is the corresponding average value. Integrals were numerically
calculated. To reduce errors due to sampling noise at least 100 average (per cycle) values were
acquired and then the mean values were calculated.
15
1.10 Perturbation/Observation algorithm
The perturbation observation (P/O) algorithm for maximum power point tracking (MPPT)
was used to optimize MFC performance during the tests with a fixed external resistor (control
tests) and between frequency and duty cycle tests. At each iteration, the P/O algorithm modified
Rext (digital potentiometer) with a predetermined amplitude (∆R) at each iteration. The direction
of resistance change was selected by comparing the value of the power output with that at the
previous resistance. Once the algorithm converges to a vicinity of the optimum resistance value,
the Rext will oscillate around this optimum with a maximum distance of ∆R. A computer-
controlled digital potentiometer with a resistance variation range from 4 to 130 Ω and a step of
1.25 Ω was used (Innoray Inc, Montreal, QC, Canada). A detailed description of the P/O
algorithm can be found in (Woodward, Perrier, & Srinivasan, 2010).
1.11 Numerical methods
Computer simulations were carried out using the equivalent circuit model and model solutions
described in this document. Parameter estimation was carried out using Fmincon function of
Matlab R2010a (Mathworks, Natick, MA, USA). In the parameter estimation procedure the root
mean square error (RMSE) between the model outputs and measured values of UMFC was
minimized using data of five on/off cycles. At an R-PWM frequency of 0.1 Hz this corresponded
to 637 data points. At a frequency of 100 Hz, 1000 data points were used to estimate model
parameters.
16
CHAPTER 4 MFC OPERATION WITH PULSE-WIDTH MODULATED
CONNECTION OF REXT
1.12 Frequency Characterisation of MFCs
In order to evaluate the effect of a pulse-width modulated connection of the external
resistance (R-PWM mode of operation), MFC-1 and MFC-2 were operated at several frequencies
ranging from 0.1 Hz to 1000 Hz. At each tested frequency, was connected to the MFC
during the first half of the cycle and disconnected for the rest of the cycle, thus corresponding to a
duty cycle of 50%.
Figure 2A shows the average output voltage ( ) calculated over the external resistor
( ) of MFC-1 during the R-PWM tests. The frequency tests were carried out with values
of 8 and 47 . It can be seen that in all tests the average voltage increased with the initial
frequency increase, then a plateau was reached at around 100-500 Hz.
Figure 2. Average external voltage ( ) as a function of Rext connection / disconnection
frequency. A – MFC-1 tests with 15 min and 1 h intervals between frequency changes; B – MFC-
2 tests performed with frequency changes at 1 h intervals.
Initially, frequency tests were carried out with 15 min intervals between each frequency
change. The tests were also repeated with 1 h intervals between the changes. Figure 2A shows a
comparison of profiles obtained with 15 min and 1 h intervals. It may be appreciated that
profiles area qualitatively similar dependence. However, the average voltage was always higher
in the tests carried out with 1 h intervals, i.e. the average (per cycle) power output was improved.
0.08
0.12
0.16
0.2
0.24
0.1 1 10 100 1000
Vo
ltag
e (
V)
Frequency (Hz)
A
Rext = 47 Ω (15 min interval)
Rext = 8 Ω (1 h interval)
Rext = 8 Ω (15 min interval)
0.09
0.11
0.13
0.15
0.17
0.19
0.1 1 10 100 1000
Vo
lta
ge
(V
)
Frequency (Hz)
B
Rext = 12 Ω (1 h interval)
Rext = 7.5 Ω (1 h interval)
17
This suggests that a 15 min interval was insufficient to establish steady-state conditions
corresponding to a new operating frequency. Also, it appeared that the R-PWM mode of
operation led to an overall performance improvement, as power outputs were consistently higher
as compared to a fixed . To insure reproducibility, the frequency tests were repeated in MFC-
2 with values of 7.5 and 12 .
Once again, a similar trend was observed with a near linear increase of as the
operating frequency increased from 0.1 Hz to 500 Hz (
Figure 2B). This increase in average voltage and, accordingly, in average power output
was followed by stabilization at around 100-500 Hz.
1.13 Dynamic Response of MFCs at Low and High Frequency
MFC response to periodic connection/disconnection of was also characterized by
observing the dynamics of MFC output voltage ( ) during each cycle. Figure 3 compares
values acquired during MFC-1 operation at a low frequency of 0.05 Hz (Figure 3A,
D=75%) and at a high frequency of 100 Hz (Figure 3B, D=90%).
Figure 3. Profiles of MFC voltage ( ) measured at connection / disconnection
frequencies of (A) 0.05 Hz (D=75%) and (B) 100 Hz (D=90%).
It should be understood that when is connected, the output and external voltages are
equal, i.e. = . However, if is disconnected, then = 0, while > 0. At
both frequencies, MFC output voltage ( ) abruptly decreases when is connected (closed
circuit with switch ON), while it increases when is disconnected (open circuit with switch
0.1
0.2
0.3
0.4
0 20 40 60 80
MF
C o
utp
ut
vo
lta
ge
(V
)
Time (s)
A
model output
measurements
0.1
0.2
0.3
0.4
0 5 10 15 20 25
MF
C o
utp
ut
vo
ltag
e (
V)
Time (ms)
Bmodel output
measurements
18
OFF). Also, when is connected to the MFC, current demand increases and a voltage divider
is created between the MFC's internal impedance and the external resistance, causing to
decrease.
At 0.05 Hz two different dynamics components are evidenced during each on-off or off-
on transition (Figure 3A). At first, there is an abrupt change of until reaching some
intermediate value. This fast transition is followed by an exponential curve, which approaches the
steady-state value at a much slower rate. At a frequency of 100 Hz (Figure 3B), only fast
dynamics appear in the curve, while the slow dynamics disappears and essentially
switches between two levels, with higher voltage corresponding to the open circuit state and
lower voltage corresponding to the closed circuit state. This dynamics is consistent with the
results of the frequency tests shown in Figure 2 and can be described by a simple equivalent
circuit model (Randles model, (Randles, 1947)) previously used for modeling batteries (Durr,
Cruden, Gair, & McDonald, 2006). The same equivalent circuit model was also recently used to
simulate a MFC power management system (Yang, Zhang, Shimotori, Wang, & Huang, 2012).
The model consists of two resistors and a capacitor, which enables the description of the slow
and fast output voltage responses observed during the tests. ¡Error! No se encuentra el origen
de la referencia. shows the model diagram, where corresponds to MFC's open circuit
voltage (ideal voltage), C represents the actual MFC capacitance, accounts for the MFC's
ohmic losses, and represents the resistive component accounting for both the activation and
concentration losses (Yang, Zhang, Shimotori, Wang, & Huang, 2012).
19
1.14 The Equivalent Circuit Model Explained
Figure 4. MFC Equivalent Circuit Model (ECM)
The following first order differential equation describes voltage dynamics over the
capacitance:
(2)
where is the voltage at the internal capacitor, is the external resistance, and
is the apparent open circuit voltage. By applying Kirchhoff’s circuit law to the diagram in
¡Error! No se encuentra el origen de la referencia., the following analytical solution can be
used to obtain MFC output voltage ( ) as a function of time at low operating frequencies:
(3)
where,
(4)
Here, the capacitance final voltage Ufinal and the time constant are defined as:
(5)
VOC C
R1
R2
SW
Rext
MFC
+
-
UMFC
+
Uext
-
20
1.14.1 The High Frequency Profile
At sufficiently high frequencies of connection/disconnection, the voltage over the
capacitance is considered to be constant, as capacitance C opposes to be charged or discharged.
Current over the capacitance is supposed to be zero over a cycle of operation. Hence,
(6)
When the switch is closed (from t = 0 to t = t),
(7)
On the other hand, when the switch is open (from t = t to t = T),
(8)
In this case, voltage sign changes as capacitance is supposed to discharge through
resistance when the switch is open. When solving the latter integral, may be obtained as
a function of the duty cycle D ( ).
(9)
Then UMFC(t) can then be calculated as:
(10)
will then vary between two values: when the switch is open,
and when the switch is closed. The term I represents the closed circuit
current, which is given by:
(11)
Figure 5 illustrates an example of a experimentally obtained high frequency profile of a
MFC operated under R-PWM mode.
21
Figure 5. High frequency profile of a MFC operated under R-PWM mode
1.14.2 Power Analysis for High Frequency Operation
The optimal duty cycle can be found by substituting the capacitance voltage in
equation (10) with the expression given in equation (9). Then, current is then defined as a
function of duty cycle (D), as shown in equation (16) below:
(12)
For intermittent operation, power is defined by:
(13)
The optimal value of D at which power output reaches its maximal value can be found
from the first-order optimality condition
is evaluated. It can be seen that power output is
maximized at the following value of D.
(14)
Since under optimal operating conditions,
(15)
which implies that maximal power output is achieved at D=1 (100%), at least according
to equivalent circuit model analysis.
22
1.14.3 The Low Frequency Profile
For intermittent operation in R-PWM mode, may be equated to its true value when
the switch is closed. On the other hand, when the switch is open and no current flows through the
circuit, may be considered infinity (∞), so may be equated to zero. Besides, the RC
circuit time-constant becomes . Finally, is given by the value at which the
capacitance is charged when the switch position is commuted. Figure 6 illustrates an example of
a experimentally obtained high frequency profile of a MFC operated under R-PWM mode.
Figure 6. Voltage profile for a MFC operated at low frequency
1.15 The Proposed Equivalent Circuit as a Modeling Tool for MFCs
The proposed ECM might have a limited predictive capacity as it assumes that all the
electrical elements are constant. Furthermore, this model does not consider any changes in
biomass concentration, microbial activity, and carbon source concentration, i.e. constant values
of these parameters are assumed. The MFC internal resistance and open circuit voltage were
already demonstrated to be strongly dependent on bio-film density, on carbon source
concentration in the anodic liquid, and on temperature (Pinto R. P., Srinivasan, Manuel,, &
Tartakovsky, 2010.) (Pinto, Srinivasan, & Tartakovsky, 2011b.). Therefore, the equivalent circuit
model might be lacking the predictive capacity of bio-electrochemical models such as recently
developed two-population bio-electrochemical MFC model (Pinto R. P., Srinivasan, Manuel,, &
Tartakovsky, 2010.) and the conduction-based MFC model (Marcus et al. 2007) and cannot be
used to predict the influence of various process inputs, such as the organic loading rate and the
operating temperature, on MFC performance.
23
Nevertheless, it offers some insight on the fast process dynamics linked to the electrical
properties of a MFC. Indeed, when the electrical circuit is operated in the continuous mode (i.e.
is constant), the internal capacitor is fully charged and the total internal resistance can be
expressed as . The capacitor dynamics may only be evidenced when the system
is disturbed, for example by means of a switch operated at a low frequency.
Figure 3 compares the equivalent circuit model outputs with voltage measurements at low
(Figure 3A) and high (Figure 3B) frequencies of connection/disconnection. For this
simulation, model parameters were estimated by minimizing RMSE between the measured
voltage values and corresponding model outputs, as described above. The following parameters
were estimated : = 0.33 V, = 4.24 Ω, = 3.25 Ω, C = 0.38 F. The comparison of
simulated and measured voltage values shows that the model adequately describes process
dynamics at both frequencies, although at the high operating frequency the model appears to
somewhat underestimate the output voltage. As mentioned above, although process dynamics is
adequately described within each cycle, the model is too simplified to predict the output voltage
over extended periods of time.
Furthermore, while the equivalent circuit model analysis might suggest that the power
output is maximized at D equal to 100%, previous studies demonstrated improved MFC power
output at D values below 100%, at least when the MFC was operated at very low frequencies
below 0.1 Hz (Grondin, Perrier, & Tartakovsky, 2012). Consequently, the performance of MFC-1
and MFC-2 was evaluated in a series of tests (D - tests) performed at a frequency of 500 Hz and
various D values ranging from 5% to 100%, the latter corresponding to a fixed resistor.
1.16 Duty Cycle (D) Characterisation of the MFCs
Notably, MFC power output might also be dependent on the selected value of .
Indeed, power output is maximized if external and internal impedances are matched. Therefore,
prior to D tests total internal resistances ( ) of MFC-1 and MFC-2 were estimated by
conducting polarization tests and calculating values using linear parts of each polarization
curve. Based on this technique, both MFCs showed internal resistance values in a range of 12 -
15 Ohm.
Figure 7A shows MFC-1 power output at different values of the duty cycle and different
external resistances. When D tests were conducted with = 17 , which is slightly above the
24
estimated value of based on the corresponding polarization test, power output was
maximized at D = 95%. A duplicate test performed immediately after the first test demonstrated
excellent reproducibility. Following this test, to compare R-PWM and mode of operation with the
power output corresponding to a constant , MFC-1 was operated at D = 100% for three days.
A slow decline in power output over time was observed with the power output stabilizing at 2.23
mW (Figure 7A, D = 100%). Interestingly, a re-evaluation of Rint suggested an increase to 20 .
A third D test conducted following MFC-1 operation with a constant confirmed a power
output decrease (Figure 7A).
Figure 7. MFC Power outputs of MFC-1 (A) and MFC-2 (B) as a function of their duty cycles.
Power output at D=100% corresponds to MFC operation with fixed external resistance. All D-
tests were carried out at a frequency of 500 Hz.
D tests were also performed in MFC-2 with = 13.5 , which corresponded to an
estimated value of . In this test, MFC power output at D = 100% was estimated using the
same experimental procedure previously performed for other D values, i.e. the voltage was
measured after one hour of MFC-2 operation with a fixed resistor. Consequently, the power
output decrease at D = 100% was much lower as compared to D = 95% (Figure 7B). When the
test was repeated at = 21 , which was above the estimated value of , there was no
difference between power outputs at D = 95% and D = 100%. For the tests conducted at = 6
(well below estimation), the power output was maximized at around D = 45%, as can be
seen from the data presented in Figure 7B. Although this maximum was below the highest power
output observed at , the R-PWM mode of operation prevented a sharp drop in power
output typically observed at . and improved MFC stability by limiting the current.
0
1
2
3
4
0% 20% 40% 60% 80% 100%
Po
we
r (m
W)
Duty Cycle (%)
A
Rext = 17 Ω
Rext = 17 Ω (duplicate)
Rext = 17.5 Ω
0
1
2
3
4
5
0% 20% 40% 60% 80% 100%
Po
we
r (m
W)
Duty Cycle (%)
B
Rext = 13.5 Ω
Rext = 21 Ω
Rext = 6 Ω
25
This feature might be especially useful to prevent voltage reversal in a stack of MFCs (Oh &
Logan, 2007).
D-curves shown in Figure 7 are in agreement with the results presented by Grondin et al.
(Grondin, Perrier, & Tartakovsky, 2012), where the external load connection was governed by
the upper and lower boundaries of the MFC output voltage, thus resulting in a variable switching
frequency, which was below 0.1 Hz. Overall, D-tests suggested an increase in power output as a
result of MFC operation in R-PWM mode. To elaborate on this observation, MFC-1 and MFC-2
were operated for 3-5 days in the R-PWM mode with 95% duty cycle (100 Hz) and external
resistance values chosen based on estimations obtained in the polarization tests. Then the
operating mode was changed to constant connection and the MFCs were operated for another 3-5
days. To ensure optimal performance during this period, value was optimized in real time
using the P/O algorithm described in the Materials and Methods. This sequence of testing was
repeated several times. Power outputs obtained during each MFC operation by the P/O algorithm
were used as a basis for comparison (control) with the R-PWM mode of operation. The results of
this comparison are summarized in Table 1 (current and power outputs were estimated based on
the last 24 h of operation).
Table 1 A comparison of average currents, power outputs and Coulombic Efficiencies (CE)
obtained during - PWM and Perturbation/Observation tests carried out at two influent
acetate concentrations.
Influent
acetate
mg L-1
Cell
R-PWM mode Perturbation/Observation
current
mA
Power
mW
CE
%
current
mA
Power
mW
CE
%
900 MFC-1 16.4 3.63 91.5 14.4 2.83 80.3
900 MFC-2 13.6 3.62 76.1 14.1 2.55 78.6
1800 MFC-1 15.1 3.84 42.2 17.1 3.07 47.9
1800 MFC-2 20.6 3.60 57.6 19.6 3.46 54.9
Interestingly, similar currents (and therefore similar Coulombic efficiencies) were
observed, while both in MFC-1 and MFC-2 voltages and power outputs were consistently higher
during R-PWM tests. Since at an influent acetate concentration of 900 mg L-1
the anodic liquid
measurements showed acetate – limiting conditions with acetate levels below 40 mg L-1
, the tests
26
were repeated where the influent concentration of acetate was doubled (1800 mg L-1
). The
increased acetate load led to higher acetate concentrations in the anodic liquid (600-700 mg L-1
)
and somewhat lower Coulombic efficiency. Nevertheless, the results given in Table 1 once again
confirmed improved power output during R-PWM operation.
Overall, power outputs observed during R-PWM tests were in a range of 3.6 – 3.8 mW
corresponding to a volumetric power density of 72-76 mW L-1
. This power density is not only
higher than that observed during MFC operation using the P/O algorithm (2.6 – 3.5 mW or 51-70
mW L-1
, Table 1), but also is higher in comparison to the recently reported performance of a
continuously operated MFC with a power density of 30-50 mW L-1
(Ahn & Logan, 2012).
Interestingly, the periodic and pulse modes of operation of catalytic reactors were
observed to lead to an increased catalyst activity and therefore an increased volumetric
performance (Silveston, Hudgins, & Renken, 1995). Several mechanisms were proposed to
explain the increased catalyst activity, including a change in the catalyst state in response to
reactant concentration, a higher catalyst activity due to a transient state, and non-linear reaction
kinetics (Roopsingh & Chidambaram, 1999); (Silveston, Hudgins, & Renken, 1995)). While a
direct comparison between the periodic operation of chemical reactors and the R-PWM mode of
MFC operation might not be always justified, both systems feature catalysts with non-linear
reaction kinetics. Hence, it can be suggested that at high-frequencies the R-PWM mode of MFC
operation leads to a reduced activation and/or concentration losses due to changes in the bio-
catalytic activity.
These losses are represented as in the equivalent circuit model (¡Error! No se
encuentra el origen de la referencia.). Also, it can be suggested that the carbon source
concentration increases when is disconnected. Considering poor mixing within the carbon
felt anode, carbon source (acetate) transport through the porous anode might be one of the
important limiting factors, i.e. acetate concentration within the anode is expected to be
significantly lower than its concentration in the bulk anodic liquid.
disconnection prevents acetate consumption by anodophilic microorganisms.
Consequently, if is disconnected, acetate concentration within the anode might increase to
approach its level in the bulk liquid. Several previous studies demonstrated a strong link between
carbon source availability and MFC performance, including the effect of carbon source on
27
values (Martin, Savadogo, Guiot, & Tartakovsky, 2010) (Pinto R. , Srinivasan, Guiot, &
Tartakovsky, 2011a)). As metabolic activity of the anodophilic microorganisms resumes upon
reconnection, the improved acetate availability positively affects MFC performance.
Indeed, the anodophilic microorganisms were shown to exhibit a non-linear (Monod or Haldane-
like) kinetics of carbon source consumption with lower internal resistances observed at carbon
source – non-limiting conditions (Hamelers, Ter, Stein, Rozendal, & Buisman, 2011); (Marcus,
Torres, & Rittmann, 2007); (Manohar A. K., 2009); (Pinto R. P., Srinivasan, Manuel,, &
Tartakovsky, 2010.)). These hypotheses might require extensive validation using experimental
methods such as electrode potential monitoring and EIS measurements (Martin E., 2013)
followed by a thorough model-based analysis.
28
CHAPTER 5 ECM APPLICATION FOR ONLINE MONITORING AND
PARAMETER ESTIMATION OF A MFC
Commonly, electrical properties of bio-electrochemical systems are measured by means
of off-line electrochemical methods like polarization curves or cyclic voltammetry. Although
these methods provide highly accurate measurements for electrical parameters like internal
resistance and capacitance, they require the system to be taken off-line for the measurement to be
accurate.
Looking forward to applying well-known process control strategies to the enhancement of
MFCs' performance, it is necessary to count on monitoring strategies that allow the online
estimation/calculation of the MFCs internal parameters. Hence, the study of an online monitoring
and parameter estimation strategy is presented hereafter.
This online monitoring procedure is based on both the proposed equivalent circuit model
(ECM), and the low and high frequency profiles described previously. To start, the online
monitoring strategy is developed. Afterwards, the laboratory tests are described. Finally, the
results are presented and compared to previously developed off-line parameter estimation
strategies.
1.17 Monitoring Procedure: from Electrical Modeling to Online Monitoring
Tool
The analytical solution described before for the ECM can be used for online estimation of
key process parameters, such as R1, R2, C, and Uoc. In the proposed procedure, R1 is first
estimated during MFC operation at high frequency (e.g. equal or above 100 Hz). Under these
conditions Uc is assumed to be constant. Afterwards, Uoc is estimated by letting the MFC run in
pseudo-open-circuit mode (Rext not connected for limited time). Finally, R2 and C are estimated
when the MFC is operated at a low frequency (e.g. below 1 Hz).
In more details, at high operating frequencies UMFC is assumed to be at either high ( )
or low ( ) levels. With respect to voltage profile in ¡Error! No se encuentra el origen de la
referencia., the two voltage levels are related as follows:
29
(16)
Notably, Ulow and Uhigh are measurable values, and Rext is known. Hence Eq. (16) can be
used for R1 estimation. Subsequently, Uoc estimation can be obtained by operating the MFC in the
open circuit mode for a short period of time, e.g. 60 s. In this case, Uoc could be assumed to be
equal to the voltage at the end of the “open circuit” part of the cycle.
Furthermore, R2 and C estimations can be also obtained using voltage measurements at
low operating frequencies (e.g. T = 60 s). If the duty cycle is set at 80% in a 60 s cycle, the switch
remains close during 48 seconds, making UMFC decrease to a pseudo steady state value, called
Ufinal in Figure 8. To facilitate the parameter estimation procedure, it is assumed that the MFC
reaches a steady state voltage after 48 seconds, i.e. at the end of the cycle part with connected
Rext.
Figure 8. UMFC profile at low frequency operation
The value of R2 may then be obtained from Equation (5), as Ufinal is established
experimentally, and the values for R1 and Uoc have previously been estimated.
Finally, for the estimation of C, the value of is first established. To do so, it is calculated
following the criteria that defines as the time that takes an exponential response to achieve the
63% of the total voltage variation. In this case, the exponential response corresponds to the
impact of the capacitance dynamic behaviour over UMFC, as shown in Equations (4), and (10).
30
In Figure 8, the exponential voltage variation is called ∆U. The fast variation of the
voltage before the exponential part is not taken into account for the calculation of ∆U, as this
abrupt change is attributed to the fact that the capacitance voltage does not change immediately,
once the current is abruptly changed. Once is estimated, the value of C may be calculated from
Equation (5). Five low frequency cycles are acquired, so R2 and C are calculated as an average of
the values calculated for each cycle.
1.18 Parameter Estimation and Online Monitoring Tests
To demonstrate the on-line parameter estimation procedure and compare the on-line and
off-line estimations (obtained at the end of each experiment, two different tests were developed
using two different MFCs.
The first test comprises the on-line monitoring and parameter estimation of a mature MFC
operated at several influent concentrations of the carbon source (acetate). The second test
involves monitoring of MFC start-up over time, from its inoculation to steady-state performance.
For this purpose, the monitoring and parameter estimation procedure described above was
implemented for a MFC which was started up and operated using the R-PWM mode.
Off-line computer simulations were carried out using the equivalent circuit model to
compare the proposed on-line monitoring strategy to previously developed off-line estimated
procedures. Off-line parameter estimation was carried out using Matlab R2010a (Mathworks,
Natick, MA, USA). The root mean square error between the model outputs and measured values
of UMFC was minimized using data of five on/off cycles obtained during both low and high
frequency MFC operation. All four ECM parameters were estimated when offline parameter
estimation was executed using fmincon.
1.18.1 MFC Internal Parameters Variation as a Function of Organic Load
MFC-1 was used for on-line parameter estimation in tests with the organic load changes
imposed approximately every 3.5 days. Initially, influent concentration was set to a low value of
450 mg L-1
. It was then increased with step changes of 450 mg L-1
, until a maximum
concentration of 1800 mg L-1
was reached. Subsequently, influent concentration was decreased
with the same step change until reaching once again a minimum influent concentration of 450 mg
L-1
. An influent concentration of 450 mg L-1
corresponds to an organic load of 70.65 mg d-1
31
(hence, an acetate flow rate of 0.075 mL h-1
). The resulting profile of acetate flow rate is shown
in Figure 9.
Figure 9 Flow rates of acetate stock solution
The on-line parameter estimation procedure was executed every hour, while low and high
frequency profiles for UMFC were acquired every 6 hours. These profiles were later used for off-
line estimations.. Polarization tests were also conducted prior to each change in influent
concentration. Besides, cyclic voltammetry tests were also carried out in order to estimate the
MFC capacitance.
1.18.1.1 UMFC profiles obtained using on-line and off-line ECM parameters
As it may be seen from the ECM analytical solutions described above, low and high
frequency profiles are correlated, as values calculated at low frequency are dependant of values
calculated at high frequency. Hereafter, it is shown how UMFC profiles generated from the
estimated internal parameters match the actual MFC voltage profile at low and high frequencies,
hence validating the proposed online monitoring approach.
Figure 10 and Figure 11 show UMFC profiles obtained from offline simulations using
MATLAB®. Each figure is divided into four subsections as follows:
1. Offline estimated parameters: A) UMFC at low frequency, and B) UMFC at high frequency,
2. Online estimated parameters: C) UMFC at low frequency, and D) UMFC at high frequency.
32
Figure 10 UMFC voltage profiles at nominal or higher influent concentration (≥ 900 mg L-1
)
As shown in Figure 10, for influent concentrations greater than the nominal value at
which MFC was operated (900 mg L-1
), UMFC profiles generated from online estimations proved
to better match the UMFC low and high frequency profiles than the profiles generated from offline
estimated parameters. Table 2 shows a comparison of both parameter estimation procedures
based on the calculation of Mean Square Errors (MSE) for each graphic in Figure 10. In the case
of low frequency profiles, MSE is always smaller for offline parameter estimation. Although,
online parameter estimations always proved a smaller MSE at high frequencies. As it will be
discussed later, deviations were encountered in the estimations for R2 and C.These deviations
cause hence the differences in the calculated profiles.
Table 2 Mean Square Errors for UMFC estimated profiles at different organic loads
Mean Square Error (MSE)
Offline Estimation Online Estimation
Figure A B C D
10 2.937E-05 5.260E-04 1.169E-04 9.690E-06
11 6.555E-04 3.072E-04 1.965E-03 4.500E-05
At low influent concentration, the proposed online parameter estimation strategy does not
perform as well as the offline strategy. Added to inaccuracies caused by noise in the data
acquisition when treating low power signals at high frequency, the procedure lacks a capacity to
33
replicate the low frequency profile, as capacitance values seem to be overestimated, which causes
the time constant value to increase.
As is overestimated, the model might be slower than the actual dynamics (Figure 11C).
On the other hand, offline estimation prove a better capacity to replicate low frequency profiles at
low influent concentration (Figure 7A), although the estimation of the high frequency profile still
proves to be poor (Figure 7B).
Figure 11 UMFC voltage profiles at low influent concentration (450 mg L-1
)
1.18.1.2 Comparison of On-line and Off-line Estimated Parameters
Figure 12 compares R1 estimations obtained following the on-line estimation procedure
described above with the results of the off-line parameter estimation. With an exception of a short
period following MFC operation at low influent concentration (around t = 700 h), there was a
good agreement between the two estimation methods. Interestingly, there was no immediate
effect of influent acetate concentration (influent concentration) on the estimated R1 value.
However, MFC operation with progressively increasing influent concentrations between t = 100
h and t = 500 h led to lower R1 values. Sharp decreases were observed around t = 180 h and then
around t = 300 h (Figure 12). Shortly after the start-up of MFC operation at low influent
concentration (around t = 600 h), the off-line identification procedure indicated R1 increase, while
the on-line estimation showed no significant impact (Figure 12). Both methods detected R1
34
increase at around t = 850 h, which was not directly associated with a change in influent carbon
source concentration.
Figure 12 Results for on-line and off-line estimation of R1
Analysis of R2 estimations shown in Figure 13 suggested a strong link of this parameter
with acetate availability in the anodic liquid. Progressive increase of the influent concentration
starting from t = 100 h (Figure 13) resulted in lower values of R2 and this trend was confirmed
both by on-line and off-line estimations. Similarly, influent concentration decrease at around t =
600 h led to almost immediate increase in R2. Interestingly, R2 is often associated with activation
losses at the anode (Yang, Zhang, Shimotori, Wang, & Huang, 2012). High activation losses
might be expected at low acetate concentrations (low influent concentrations) due to carbon
source - limited metabolism of anodophilic microorganisms.
Figure 13 Results for on-line and off-line estimation of R2
35
Furthermore, a comparison of model-based internal resistance estimations calculated as
with experimental results obtained in polarization tests is shown in
Figure 14. This comparison clearly confirmed the acceptable accuracy of online
estimations.
Figure 14 Comparison of Rint estimations (on-line and off-line) with experimentally measured
values based on polarization tests.
In addition to Rint estimations, the parameter estimation procedure demonstrated carbon
source – related changes in Uoc, as shown in Figure 15. In this case, the off-line estimation
procedure appeared to provide a somewhat better response to variations in acetate load, e.g. at t =
100h (load increase) and t = 600 h (load decrease). Nevertheless, when compared with the results
of polarization tests, both estimations were significantly lower than the Uoc values measured in
the experiment with a 30 min disconnection (open circuit) period. This is to be expected, as both
off-line and on-line estimation procedures were based on very short disconnection times during
OFF parts of the cycles, which were clearly insufficient to achieve true steady state. Also, it
should be taken into consideration, however, that long periods (dozens of minutes) of MFC
operation with a disconnected external resistance might lead to carbon source accumulation in the
anodic liquid, which in turn is expected to affect (increase) Uoc estimations.
36
Figure 15 Results of on-line and off-line estimation of Uoc.
Estimated capacitance values were also studied. As can be seen in Figure 16, offline
parameter identification always gave lower capacitance values than the on-line monitoring
strategy proposed. Additionally, the variability of the estimated values was greater. Interestingly,
online monitoring, showed that when influent concentration was decreased to a value lower than
the nominal (< 900 mg L-1
), a fast increase in capacitance was encountered in response to such
change (at times ~0 hours, and ~600 hours in Figure 16). If this response is associated to
microbial capacity to storage energy, microbes seem to store as much energy as possible as
carbon source is decreased and available food source is scarce. A subsequent decrease is also
observed.
When influent concentration is equal or greater than the established nominal influent
concentration (≥ 900 mg L-1
), capacitance is not greatly affected. This can be seen in the period
between 150 hours and 600 hours in Figure 16. This is also confirmed by offline estimations,
although the variability of the calculated parameter is greater for this period.
Finally, both online and offline estimations parameters showed a fast increase in the
capacitance value when organic load was changed from low to nominal (~650 hours). Once
again, as microorganisms seem to store energy after a period of famine, capacitance seems to
increase as a representation of this biologic response occuring in the bioreactor. Once again,
capacitance decreases after the initial increase, appearing to settle down at ~1000 hours.
37
Figure 16 Results of online and offline estimation of C.
Table 3 shows standard deviations calculated for both online and offline estimations. As it
can be seen, standard deviations are statistically similar, which proves the capacity of both the
online and offline methods to represent MFC dynamics.
Table 3 Summary of Standard Deviations for Online and Offline Estimations
Standard Deviation for Estimated Parameters
Parameter Online Estimations Offline Estimations
R1 (Ω) 1.10 1.02
R2 (Ω) 6.10 6.61
Rint (Ω) 6.10 6.94
C (F) 0.10 0.16
Uoc (V) 0.01 0.04
1.18.2 MFC Internal Parameters Variation as a Function of Time
MFC-2 was used to follow variation of key MFC parameters over time. For this test, a
new anode was installed and MFC-2 was inoculated with the effluent of MFC-1. MFC-2 was
operated at a nominal influent concentration of 900 mg L-1
, and the start-up procedure involved
the intermittent operation of the MFC (D = 85%, Frequency = 100 Hz), and the hourly execution
of the online monitoring strategy. For this second test, UMFC voltage profiles were acquired every
18 hours, and polarization tests were performed every 3 to 5 days. The test was carried out for a
month, although the MFC showed signs of mature behaviour after 20 days of operation.
38
1.18.2.1 The Evolution of UMFC Voltage Profiles in Time
Figure 17 to Figure 19 show UMFC profiles obtained from offline simulations using
MATLAB®. Once again, each figure is divided into four (4) as explained in 1.18.1.1. Once
again, despite the inaccuracies caused by the measurement of low power signals when the MFC
start-up just began, UMFC profiles generated from on-line estimated parameters provided a better
match to experimentally measured values.
Figure 17 UMFC voltage profiles 18 hours after the MFC start-up.
Figure 18 UMFC voltage profiles 1 week after the MFC start-up.
39
One week after the start-up, generated profiles showed the same behaviour as when
influent concentration was ≥900 mg L-1
. Hence, both parameter estimation strategies prove their
capacity to replicate the profiles at low frequency, while the online monitoring strategy proves a
to be a better tool to describe operation at high frequency. Twenty days after the MFC start-up,
both parameter estimation procedures yielded similar results as shown in Figure 19. Table 4
shows MSE calculations for Figures 17, 18, and 19. Once again, offline parameter estimation
shows smaller MSE values at low frequency, while MSE values at high frequency are smaller in
the case of online parameter estimation.
Figure 19 UMFC voltage profiles 20 days after the MFC start-up.
Table 4 Mean Square Errors for UMFC estimated profiles during organic maturation of MFC
Mean Square Error (MSE)
Offline Estimation Online Estimation
Figure A B C D
17 3.715E-06 1.659E-03 1.841E-05 1.513E-05
18 5.347E-05 9.656E-04 2.026E-04 4.866E-05
19 2.122E-05 3.445E-04 7.697E-05 2.333E-05
As stated earlier in this document, one of the major challenges in bio-processes control is
the development of sensors with the capacity for non-disruptive online monitoring.
40
The capacity of the proposed monitoring strategy to replicate the MFC electrical
dynamics based on a simplified ECM opens the door to its application as a periodic follow-up
sensor. Hereafter, a study of the evolution of the MFC internal parameters in time is presented.
1.18.2.2 Evolution of MFC Internal Parameters Over Time
During MFC-2 start up, internal electrical parameters were estimated every hour. Based
on the values obtained, the evolution of these parameters in time was studied. Once again, UMFC
profiles generated from these parameters validate that the ECM is capable of replicating the MFC
electrical dynamics.
Figure 20 shows the evolution of R1 and R2 over time. In general, R1 values obtained from
offline parameter identification were greater than those calculated from the online monitoring
strategy, while values for R2 were lower. As it could be expected, R1 and R2 values decrease in
time. Values for R2 were always greater than for R1, while fairly constant values were achieved
after 200 hours for R1 and after 500 hours for R2.
Apparently, ohmic losses (R1) reach a steady-state value faster than activation and
concentration losses (R2). As activation and concentration losses are associated with bacteria
growth and carbon source consumption, thus this kind of response over time for these two MFC
internal parameters might be expected. As bacteria living cycle establishes until reaching
matureness, R2 values decrease.
Figure 20 R1 and R2 evolution in time.
Internal resistance, calculated as the sum of R1 and R2, was compared to the values
obtained by means of polarization curves. As can be seen in Figure 21, experimental Rint values
41
match well both off-line and on-line estimations. Although during 400 hours, values for Rint
obtained from polarization curves and from the ECM estimations match well, after 400 hours ,
values calculated from the polarization curves seem to be generally greater.
As explained before, the effect of relatively long periods (dozens of minutes) of MFC
operation with a disconnected external resistance may lead to carbon source accumulation in the
anodic liquid, which alters bacteria behaviour, represented in the ECM by R2, and which in turn
is expected to alter the measurements for Rint during polarization curves tests.
Figure 21 Rint evolution in time.
Figure 22 UOC evolution in time.
In the case of UOC online monitoring (¡Error! No se encuentra el origen de la
referencia.), a fast increase was evidenced after the start up and until ~100 hours of operation.
Subsequently, the value decreased almost exponentially until reaching a stable value, which was
42
always lower than that obtained from the polarization curves. Once again both internal parameter
estimation methods gave similar results.
Finally, the evolution in time of parameter C was also studied, as shown in Figure 23. In
this case, it was the online parameter identification routine which proved a higher variability. As
it could be expected, both estimation methods showed that capacitance increases as microbial
activity does. As a fact, as more bacteria grow inside the bioreactor, the greater its capacity to
storage energy, what validates once again the capacitance C as a parameter that allows the
follow-up of microbial activity for a process control purpose.
Figure 23 Capacitance C evolution in time.
43
CHAPTER 6 CONCLUSION AND RECOMMENDATIONS
1.19 Conclusions
MFC operation with pulse-width modulated connection of the external resistor (R-PWM
mode) increased the average output voltage and the power output at operating frequencies above
100 Hz. By comparing power outputs of MFCs operated in the R-PWM mode and with a
constant resistance equal to the estimated total internal resistance value, the R-PWM mode
operation was demonstrated to improve MFC performance by up to 22-43%.
Analysis of the output voltage profiles acquired during R-PWM tests showed the presence
of slow and fast dynamic components. This process dynamics was successfully simulated by a
simple equivalent circuit model consisting of two resistors and a capacitor.
Furthermore, based on this simplified equivalent circuit model, an online parameter
estimation strategy was implemented to periodically estimate key MFC parameters such as
internal resistance, internal capacitance, and open circuit voltage. The feasibility of the proposed
on-line monitoring approach was confirmed by low mean square errors (5.26E-4 for low
frequency profiles, and 9.69E-6 for high frequency profiles) obtained in two laboratory trials.
Using this simple equivalent circuit model as a primary tool to develop an online
estimation algorithm opens the door to further optimization of the MFCs both as a power supply
or a wastewater treatment bio-system. Even if the accuracy of online estimations cannot be
always verified by means of offline bio-electrochemical methods due to their interference with
normal process operation, the proposed algorithm gives the capacity to follow the trends in
internal parameters not only as a function of time, but also as a function of organic load
variations and other external disturbances.
It is important to note that although the ECM provided adequate approximation of MFC
dynamics, it lacks the capacity for long-term prediction of MFC power output (e.g. days) because
it does not consider the influence of carbon source concentration and other external factors on
electricity production. Furthermore, the ECM was unable to account for enhanced MFC
performance at high switching frequencies. This can be seen from the comparison of MFC power
outputs during operation at D=100% over a period of 2 days and at various switching
frequencies, as shown in Figure 7. Higher power outputs were achieved at D values below 100%,
44
which is contrary to ECM analysis, which predicted optimal performance at D=100%. This
necessitates a more detailed study on the impact of high frequency operation on MFC
performance.
1.20 Recommendations
1.20.1 Characterisation of MFC performance under a wider range of frequencies
From an electrical engineering point of view, PWM is a method applied in order to
regulate power to a fixed load. It is well known that power can only be maximized when D =
100%. However, in the case of MFC operation, power increased at D values below 100%.
In physiotherapy, the effect of ultrasound over living human cells has been well studied.
Actually, it is well known that the application of different frequencies may have different effects
on living cells. Biologists, microbiologists, and biophysicists might combine their efforts in the
quest to understand bacteria performance under the effect of periodic current. The observed
phenomena described in this study might be better understood and used to optimize the MFCs as
a wastewater treatment tool.
1.20.2 The online monitoring strategy as a sensor for process control
Although the study of time dependant dynamics of the MFC/ECM internal parameters in
response to the step changes in organic load was not in the scope of this research, these dynamics
can be characterised by well-known dynamic modeling strategies, such as those using first-order
models with delay.
Based on these dynamic models, PI or PID controllers can then be tuned in order to
control the internal parameters while manipulating the organic load fed to the bioreactor. The
control loop would consist of:
Measurement (Sensor): In order to measure the controlled variable (any internal
parameter), the online monitoring algorithm could be used as a basis.
Decision (Controller): A digital controller whose can actually be variable. This
parameter is meant to be variable so estimates for the parameters can be calculated
at different time intervals, and the controller would still have the capacity to
compute the integral and derivative actions.
45
Action (Final Control Element): An action can be taken each time a measure is
executed. In this case, a dosage pump could be used, so organic load can be
manipulated as a function of the flow (organic load) feeding the bioreactor.
A personal quote
Quantum physics pushed the evolution of several physics principles in a way that the
human being was no longer considered to live in a world of separateness, but in a world of
relationships. At the same time, science passed from being predictable (deterministic) to become
pure potential (hence, statistical).
Basically, according to quantum physics, everything in this world seems to be
interrelated. So, maybe, the study of living systems not only involves the application of well-
known physical and engineering principles, but also of those principles that are used in daily
human relationships... specially one that all living species seem to enjoy: LOVE!
Despite the initial uncertainty of working with an unknown system, I loved my work with
both Margarita (MFC-1) and Juanita (MFC-2), and maybe just in response to the passion I proved
(talking to them, playing music for them, sometimes even dancing to them), they gave me all the
beautiful (and interesting) results included in this document. Maybe, just maybe, nature is only
waiting for human species to understand that bio-systems are living species willing to serve our
purpose.
Although, as the interaction of interrelated species, love will have to become a headstone
in the understanding of all biology 'equations'. Of course, modeling love seems a bit of a
challenge (for now!), but for sure, lots of love can be given to those magic bacteria who have
already proven their capacity to treat water, while they recover electrical energy out of 'waste'.
46
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